Question

write the coordinates of the vertices after a translation 11 units left and 1 unit down.
s(□,□)
t(□,□)
u(□,□)
v(□,□)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( S \): \( (5, 3) \) (since it's 5 units right on x - axis and 3 units up on y - axis)
• \( T \): \( (8, 3) \)
• \( U \): \( (10, 7) \)
• \( V \): \( (7, 7) \)

Step2: Apply translation rules

The translation is 11 units left (which means subtract 11 from the x - coordinate) and 1 unit down (subtract 1 from the y - coordinate). The translation rule for a point \((x,y)\) is \((x - 11,y - 1)\).

For \( S(5,3) \):

New \( x \) - coordinate: \( 5-11=-6 \)
New \( y \) - coordinate: \( 3 - 1 = 2 \)
So, \( S'=(-6,2) \)

For \( T(8,3) \):

New \( x \) - coordinate: \( 8-11=-3 \)
New \( y \) - coordinate: \( 3 - 1 = 2 \)
So, \( T'=(-3,2) \)

For \( U(10,7) \):

New \( x \) - coordinate: \( 10-11=-1 \)
New \( y \) - coordinate: \( 7 - 1 = 6 \)
So, \( U'=(-1,6) \)

For \( V(7,7) \):

New \( x \) - coordinate: \( 7-11=-4 \)
New \( y \) - coordinate: \( 7 - 1 = 6 \)
So, \( V'=(-4,6) \)

Answer:

\( S'(-6, 2) \)
\( T'(-3, 2) \)
\( U'(-1, 6) \)
\( V'(-4, 6) \)